Chapter 5, Problem 4E

(Least Squares Circles) The parametric equations for a circle with center $\left(3,1\right)$ and radius 2 are $x=3+2\cos ty=1+2\sin t$
Set $t=0:.5:6$ and use MATLAB to generate vectors of x and y coordinates for the corresponding points on the circle. Next, add some noise to your points by setting
$x=x+0.1*\text{rand}\left(1,13\right)$
and
$y=y+0.1*\text{rand}\left(1,13\right)$
Use MATLAB to determine the center c and radius r of the circle that gives the best least squares fit to the points. Set
$\begin{array}{l}t1=0:0.1:6.3\\ x1=c\left(1\right)+r*\cos \left(t1\right)\\ y1=c\left(2\right)+r*\sin \left(t1\right)\end{array}$
and use the command
$\text{plot}\left(\text{x}1,\text{y}1,\text{x},\text{y},\text{'}\text{x}\text{'}\right)$
to plot the circle and the data points.